The co-ordinates of a moving particle at any time 't' are given by `x = alphat^(3)` and `y = betat^(3)`. The speed of the particle at time Y is given by :

Options

A. `sqrt(alpha^(2) + beta^(2))`
B. `3tsqrt(alpha^(2) + beta^(2))`
C. `3t^(2)sqrt(alpha^(2) + beta^(2))`
D. `t^(2)sqrt(alpha^(2) + beta^(2))`

Answer

C

Explanation

Here `v_(x)=dx/dt=3alphat^(2)`
`v_(y)=(dy)/(dt)=3betat^(2)`
`:.|v|=sqrt(v_(x)^(2) + v_(y)^(2))`
`=3t^(2)sqrt(alpha^(2)+beta^(2))`